BREBIS non$-$dividend stock price is currently $$80.$ The risk$-$free rate $($all maturities$)$ is $2\%$ per year with continuous compounding. Use a three$-$step tree to value:

I. An eighteen$-$month European call option with strike price $$76.$ Required to design a three$-$step tree and include the prices of the stock and the value of the option on every node.

II$.$ The percentage up movement: $1,1500$

III. The percentage down movement: $0,8695$

IV$.$ What is the probability of an up movement in a risk$-$neutral world? Required the calculation.

V$.$ What is the probability of a down movement in a risk$-$ neutral world?

Required the calculation.

VI$.$ Proof that call$-$put parity works.